Illustration of Level Set and Gradient
Here f (x,y,z) = x2 - y2 - z. We consider the level set Lf(0) of f at level 0. It is a saddle surface in R3. The point a is a solution of the level set equation
f (x,y,z) = x2 - y2 - z = 0.
The level set of the derivative f '(a) at level 0 is the tangent plane to the saddle Lf(0) at the point a.Return to the main document on the implicit function theorem.